## A new Lehmer pair of zeros and a new lower bound for the de Bruijn-Newman constant Λ

G. Csordas, A. M. Odlyzko, W. Smith, and R. S. Varga

### Abstract

The de Bruijn-Newman constant $\Lambda$ has been investigated extensively because the truth of the Riemann Hypothesis is equivalent to the assertion that $\Lambda \leq 0$. On the other hand, C. M. Newman conjectured that $\Lambda \geq 0$. This paper improves previous lower bounds by showing that $-5.895 \cdot 10^{-9} < \Lambda.$ This is done with the help of a spectacularly close pair of consecutive zeros of the Riemann zeta function.

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### Key words

Lehmer pairs of zeros, de Bruijn-Newman constant, Riemann Hypothesis.

### AMS subject classifications

30D10, 30D15, 65E05.

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